Entropic sampling via Wang-Landau random walks in dominant energy subspaces

Abstract

Dominant energy subspaces of statistical systems are defined with the help of restrictive conditions on various characteristics of the energy distribution, such as the probability density and the forth order Binder's cumulant. Our analysis generalizes the ideas of the critical minimum energy-subspace (CrMES) technique \cite{malakis04}, applied previously to study the specific heat's finite-size scaling. Here, we illustrate alternatives that are useful for the analysis of further finite-size anomalies and the behavior of the corresponding dominant subspaces is presented for the 2D Baxter-Wu, the 2D and 3D Ising models. In order to show that a CrMES technique is adequate for the study of magnetic anomalies, we study and test simple methods which provide the means for an accurate determination of the energy - order-parameter ($E-M$) histograms via Wang-Landau random walks. The 2D Ising model is used as a test case and it is shown that high-level Wang-Landau sampling schemes yield excellent estimates for all magnetic properties. Our estimates compare very well with those of the traditional Metropolis method. The relevant dominant energy subspaces and dominant magnetization subspaces scale as expected with exponents $\alpha /\nu$ and $\gamma /\nu$ respectively. Using the Metropolis method we examine the time evolution of the corresponding dominant magnetization subspaces and we uncover the reasons behind the inadequacy of the Metropolis method to produce a reliable estimation scheme for the tail-regime of the order parameter distribution.

32 pages, 12 figures, version as accepted for publication to Phys. Rev. E

References in corpus (2)

• Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
• Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling

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• Phase Diagram of the 3D Bimodal Random-Field Ising Model
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Wang-Landau study of the triangular Blume-Capel ferromagnet
• First-order transition features of the triangular Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions
• Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models
• Monte-Carlo analysis of critical properties of the two-dimensional randomly site-diluted Ising model via Wang-Landau algorithm
• Wang-Landau study of the 3D Ising model with bond disorder
• Scaling and self-averaging in the three-dimensional random-field Ising model
• Universal features and tail analysis of the order-parameter distribution of the two-dimensional Ising model: An entropic sampling Monte Carlo study
• Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions
• Universality in the two-dimensional dilute Baxter-Wu model